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Waldman began his career as an actor and producer (1935–1938) before joining the BBC Variety department in 1938. Following wartime service in the Royal Air Force Voluntary Reserve, he became the assistant Head of Variety Productions in 1948.
The British public knew him best for his work with Harry S. Pepper as presenter of the popular Monday Night at Eight radio magazine programme, which was broadcast every week live. The programme started in 1937 as "Monday Night at Seven", becoming "Monday Night at Eight" soon after the outbreak of the Second World War. It was broadcast throughout the war and continued for several years after it. Waldman's speciality was "Puzzle Corner", with a "deliberate mistake" which listeners were invited to spot in time for next week's show. Each week saw a birthday guest star allowed four wishes, and one wish came true, if it could be arranged. For example, one guest wanted to announce the trains leaving from Euston Station. Another guest, young John Clark, wanted to talk to an airline pilot live while he was in the air, and to talk to Joe Davis, his snooker hero. No problem. Unfortunately, no recordings of a whole programme have survived, although the famous signature tune "It's Monday Night at Eight O'clock" does exist in the BBC Sound Archives.
After becoming a producer in Television Light Entertainment, in 1950 Waldman rose to be the BBC's Head of Light Entertainment. He launched many of distinguished names in light entertainment, such as Julie Andrews and Morecambe and Wise.
Waldman later served as the Business Manager of BBC Television Programmes (1958–1960), General Manager of BBC Television Enterprises (1960–1963), Managing Director of Visnews (1963–1977), President of the Lord's Taverners (1966) and as a trustee of the International Institute of Communications (1975–1978).